13. how many distinct 4-letter groupings can be made with the letters from the word champion if letters may not be repeated?

N = 1680

Therefore, 1680 '4 letter groupings' can be formed from the word 'champion'

Step-by-step explanation:

Given the word 'champion' which is an 8 distinct Letter word. The number of 4 letter groupings that could be formed from it can be given by the permutation since in this case order of letters are important.

The number of distinct 4 letter groupings can be given as;

N = nPr = 8!/(8-4)!, where n= 8 and r = 4

N = 8P4 = 8!/(8-4)!

N= 8!/4!

N = 1680

Therefore, 1680 '4 letter groupings' can be formed from the word 'champion'

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: